Question: Find the greatest common factor of $30$ and $75$.
The greatest common factor (GCF) is the largest number that is a factor of both $30$ and $75$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}30 &=2\cdot3\cdot5\\\\\\\\ 75&=3\cdot5\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}30 &=2\cdot3\cdot5\\\\\\\\ 75&=3\cdot5\cdot5 \end{aligned}$ Each number shares the factors ${3}$ and ${5}$, so the GCF is $3\cdot5={15}$. The greatest common factor of $30$ and $75$ is $15$.